Small superimposed radial oscillations for a class of damaged limited elastic tubes

Small superimposed radial oscillations for a class of damaged limited elastic, incompressible, isotropic and homogeneous thick-walled circular cylindrical tube are examined. Both the damage function considered elastic depend only on first invariant $$ I_{1} $$ left Cauchy–Green deformation tensor. The present work puts some light in context surgical procedure angioplasty, used especially to treat cardiovascular diseases. Our simplified assumption allows much faster analytical computation comparably accurate results. examples three material models presented, namely Arruda–Boyce, Gent, Demiray. further investigated thin membrane, above explored. Universal relations found membranes. obtained results matched with clinical data existing literature. It appears that pressure ratio virgin arterial tissue is higher before angioplasty vice versa. A similar trend frequency also follows.